Question

Solve for v
9v^2=30v-25

Answer 1

Can some one explain how to do these?
if you subtract 9v^2 from left to right i get
\[0=-9v^2+30v-25\]
and i don't know what's next.

Answer 2

Solve the quadratic. Either by factoring or using the formula.

Answer 3

polpak i don't know how to do either one of them...
by the way which formula?

Answer 4

It doesn't look like a nice one to factor offhand so I suggest using the formula. But if you haven't learned it you may have to use the hard way.

Answer 5

\[ax^2 + bx + c =0 \implies x = {-b \pm \sqrt{b^2-4ac} \over 2a}\]

Answer 6

quadratic formula?

Answer 7

Lets see if it's easier to factor than I think.

Answer 8

Oh, ! think it is!

Answer 9

-25? i got 5/3 when i solved it the formula

Answer 10

Yeah, it's a perfect square.

Answer 11

If we multiply your equation by -1 it makes more sense.

Answer 12

a and c are 3.
b and d are -5

Answer 13

so the leading coefficient would be 9 not -9 i see.

Answer 14

We have (3v - 5)(3v - 5)

Answer 15

Foiling that out we should get what we started with.

Answer 16

If you don't know the formula though you have to figure out how to factor by hand.

Answer 17

i know the formula but you can't take a square root of a negative number. this is what i mean.
\[x=\frac{5}{3}\pm \sqrt{-1800}\]

Answer 18

oops. it's
\[\frac{ \sqrt{-1800}}{18}\]

Answer 19

\[\sqrt{b^2 - 4(a)(c)} = \sqrt{30^2 - 4(-9)(-25)}\]

Answer 20

So it's \[\sqrt{900 - 900} = 0\]

Answer 21

yeah but weren't we supposed to multiply the whole equation by -1? so we get
\[\sqrt{-30^2-4(9)(25)}\]

Answer 22

That was for factoring.

Answer 23

And even if we had it wouldn't matter because \[(-30)^2 = 30^2 = 900\]

Answer 24

i got what you got also. it ends up only
\[\frac{5}{3}\]

Answer 25

Yeah, you will get the same answer even if you multiply by -1 because the b is squared and the a times the c will keep the same sign.

Answer 26

\[\sqrt{(-30)^2-4(9)(25)} = \sqrt{900 - 900} = 0\]

Answer 27

ok
a*c=-9
ad+cb=30
b*d=-25
you wrote this above how do you get your answer or how do you factor out a polynomial with the formula that you've also wrote
\[(av^2+b)(cv^2+d)\]

Answer 28

Sorry my formula should have been:
\[(av+b)(cv+d) = 9v^2 - 30v + 25\]
Therefore
\[a\times c = 9\]\[b \times d = 25\]\[(a\times c) + (b\times d) = -30\]

Answer 29

But there's not enough equations to solve it properly. If you know for sure that a, b, c, and d are integers you can make some good guesses though.

Answer 30

For example, b and d are either 25 and 1, or 5 and 5.
c and a are either 3 and 3 or 9 and 1.
And for either pair the signs for that pair have to be the same.

Answer 31

so that way is guess and check practically?
i see

Answer 32

Ack

Answer 33

That last equation is wrong.

Answer 34

Should be
\[(a\times d) + (c\times b) = -30\]

Answer 35

Those coefficients come from the foiling process.

Answer 36

So we can see that if ad = cb we would have 2ad = -30 so ad = -15 so 5 and 3 are good choices.

Answer 37

So one of the pairs is negative, the other is positive and we're good.

Answer 38

ok thanks for your time polpak. got to run be back in 20 min. maybe some more question will arouse.

Answer 39

sure thing =)